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%I #6 Jan 29 2018 08:18:28
%S 0,0,0,0,1,0,0,3,3,0,0,2,1,2,0,0,11,4,4,11,0,0,13,3,11,3,13,0,0,34,7,
%T 23,23,7,34,0,0,65,14,72,94,72,14,65,0,0,123,35,201,255,255,201,35,
%U 123,0,0,266,89,597,666,955,666,597,89,266,0,0,499,242,1717,2720,3569,3569,2720
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .0...0..0....0....0.....0......0.......0........0.........0.........0
%C .0...1..3....2...11....13.....34......65......123.......266.......499
%C .0...3..1....4....3.....7.....14......35.......89.......242.......643
%C .0...2..4...11...23....72....201.....597.....1717......5183.....15479
%C .0..11..3...23...94...255....666....2720.....8571.....30093....106192
%C .0..13..7...72..255...955...3569...15031....61046....253624...1067751
%C .0..34.14..201..666..3569..15163...77576...375845...1886321...9434661
%C .0..65.35..597.2720.15031..77576..491338..2806944..16889645.100996053
%C .0.123.89.1717.8571.61046.375845.2806944.19329083.138482223.988954778
%H R. H. Hardin, <a href="/A298930/b298930.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4)
%F k=3: [order 18] for n>19
%F k=4: [order 60] for n>61
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..1
%e ..1..0..1..0. .0..0..0..0. .0..1..1..0. .0..1..0..1. .0..1..0..1
%e ..1..1..0..0. .0..0..0..0. .1..0..1..0. .1..0..0..1. .1..1..0..0
%e ..1..0..1..0. .1..1..1..1. .1..0..1..0. .0..1..0..1. .0..1..0..1
%e ..0..0..1..1. .1..1..1..1. .1..1..0..0. .0..0..1..1. .0..0..1..1
%Y Column 2 is A297870.
%Y Column 3 is A298254.
%K nonn,tabl
%O 1,8
%A _R. H. Hardin_, Jan 29 2018
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